Question

1. In 2010, Betty White (at age 88!) hosted an episode of Saturday Night Live, becoming the oldest host the show has ever had. Most people know that she was the oldest. However, what about the second oldest? Do people have an idea how old the second oldest guest host was? A random sample of people was taken; these people were asked two questions: what is your age (x) and what do you believe is the age of the second oldest SNL host?

Note: the second oldest SNL guest host was Miskel Spillman at age 80 (in 1977) who won a contest and is the only non-celebrity to host the show.

X	25	29	32	37	40	45	47	50	53	60	65
Y	65	72	70	80	75	70	72	73	79	82	80

1. Draw a scatterplot for this set of data

2. Find the linear correlation coefficient. Based on that value, is there evidence of a linear relationship between the variables? Explain.

3. Find the line of best fit.

4. Predict the value of y given the value of x = 40

5. Find the residual for x = 40.

Answer 1

### Answers:

a] scatterplot is attached above

b] linear correlation coefficient = 0.7191

to test the significance of linear correlation

test statistics is t =3.1047

p-value = 0.0126 <0.05

we reject the null hypothesis of non significance at 5% significanc level & conclude that there is significant linear correlation between x & y

c] line of best fit is y^ =61.1722 +0.3004x

d]for x=40

y^ =61.1722 +0.3004*40

y^ = 73.19

predicted value =73.19

d] residual =y-y^ = 75-73.19=1.81

residual =1.81